Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
312 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27164071 | C2 | semidirect |
| 2. #27164042 | C2 | semidirect |
| 3. D4⋊(C199⋊C8) | C2 | semidirect |
| 8. C4⋊(C199⋊C8) | C22 | semidirect |
| 10. C4×C199⋊C8 | C22 | semidirect |
| 52. D4×C199 | M16 | semidirect |
| 89. C199 | #1486 | semidirect |
| 140. D4 | #15691870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164071 | 2 |
| #27164042 | 2 |
| D4⋊(C199⋊C8) | 2 |
| C2×C4×D4×C199 | 2 |
| #1486 | 199 |